Description
We investigate the convergence of solutions of a stochastic 3D Navier-Stokes equations to those of the primitive
equations. We explore the impact of relaxing the hydrostatic assumption in the stochastic primitive equations by
retaining martingale terms as deviations from hydrostatic equilibrium. This modified model, obtained through a
specific asymptotic scaling accessible only within the stochastic framework, captures non-hydrostatic effects while
remaining within the primitive equations formalism. We prove that it provides a higher-order approximation of the 3D
stochastic Navier-Stokes equations.
